Heterogeneous reactor model

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas-phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only Steps 1 and 9, and the effects of Steps 2 through 8 are lumped into the pseudohomoge-neous rate expression, a, b,. ..), where a,b,. .. are the bulk, gas-phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

Horst C, Chen Y-S, Kunz U, Hoffmann U (1996) Design, modeling and performance of a novel sonochemical reactor for heterogeneous reactions. Chem Eng Sci 51 1837-1846... 

In this chapter, we first cite examples of catalyzed two-phase reactions. We then consider types of reactors from the point of view of modes of operation and general design considerations. Following introduction of general aspects of reactor models, we focus on the simplest of these for pseudohomogeneous and heterogeneous reactor models, and conclude with a brief discussion of one-dimensional and two-dimensional models. 

There are many ways that two phases can be contacted, and for each the design equation will be unique. Design equations for these ideal flow patterns may be developed without too much difficulty. However, when real flow deviates considerably from these, we can do one of two things we may develop models to mirror actual flow closely, or we may calculate performance with ideal patterns which bracket actual flow. Fortunately, most real reactors for heterogeneous systems can be satisfactorily approximated by one of the five ideal flow patterns of Fig. 17.1. Notable exceptions are the reactions which take place in fluidized beds. There special models must be developed. 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

LPCVD Reactor Models. First-Order Surface Reaction. The traditional horizontal-wafer-in-tube LPCVD reactor resembles a fixed-bed reactor, and recent models are very similar to heterogeneous-dispersion models for fixed-bed reactors (21,167,213). To illustrate CVD reactor modeling, this correspondence can be exploited by first considering a simple first-order surface reaction in the LPCVD reactor and then discussing complications such as complex reaction schemes, multicomponent diffusion effects, and entrance phenomena. 

LPCVD reactor modeling involves many of the same issues of multi-component diffusion reactions that have been studied in the past decade in connection with heterogeneous catalysis. Complex fluid-flow phenomena strongly affect the performance of atmospheric-pressure CVD reactors. Two-dimensional and some three-dimensional flow structures in the classical horizontal and vertical CVD reactors have been explored through flow visual-... 

Note that the results of our simulation via the pseudohomogeneous model tracks the actual plant very closely. However, since the effectiveness factors r]i were included in a lumped empirical fashion in the kinetic parameters, this model is not suitable for other reactors. A heterogeneous model, using intrinsic kinetics and a rigorous description of the diffusion and conduction, as well as the reactions in the catalyst pellet will be more reliable in general and can be used to extract intrinsic kinetic parameters from the industrial data. 

Industrial reactors generally operate at very high velocities (of order 1 m/s) much in excess of terminal falling velocity for at least the finest powder fractions. Powder is continually elutriated and returned to the bed via cyclones. Under these conditions there is disagreement as to whether or not bubbles retain their identity and such beds have been described as "turbulent" or "fast fluidised". What little evidence there is supports the continued existence of bubbles but now in a much disturbed or heterogeneous dense phase and with a less definite shape. Until more is known about this physical situation it is not easy to see how the bubbling bed reactor models should be modified correctly to describe this flow regime. 

Equation (45) can be solved by applying different photoreactor models. The literature reports several photochemical reactor models for both homogeneous and heterogeneous reactors [11,108,109]. In practice, annular photoreactors are often used (see Fig. 5) therefore, models for this type of reactor are considered here. For other types of reactors, attention should be given to other publications [109]. 

Chemical vapor deposition and heterogeneous catalysis share many kinetic and transport features, but CVD reactor design lags the corresponding catalytic reactor analysis both in level of sophistication and in scope. In the following we review the state of CVD reactor modelling and demonstrate how catalytic reactor design concepts may be applied to CVD processes. This is illustrated with an example where fixed bed reactor concepts are used to describe a commercial "multiple-wafers-in-tube" low pressure CVD reactor. 

A generalized method to predict the deviations of the different types of fixed-bed catalytic reactor models with respect to an heterogeneous two-dimensional model is presented. Very good agreement with numerically calculated errors is found. The differences in the responses between the one and two-dimensional versions of each type of model are analyzed. The conditions in which the different types of models should be used are discussed. 

An extensive analysis of the behaviour of different types of non-adiabatic fixed bed reactor models is carried out and the importance of the heterogeneous one and two-dimensional models III-0 and III-T is stressed. Although in these models the heat and mass transfer phenomena are correctly taken into account, they... 

If the catalyst is dispersed throughout the pellet, then internal diffusion of the species within the pores of the pellet, along with simultaneous reaction(s) must be accounted for if the prevailing Thiele modulus > 1. This aspect gives rise to the effectiveness factor" problem, to which a significant amount of effort, summarized by Aris ( ), has been devoted in the literature. It is important to realize that if the catalyst pellet effectiveness factor is different from unity, then the packed-bed reactor model must be a heterogeneous model it cannot be a pseudohomogeneous model. 

When gum formation proceeds, the minimum temperature in the catalyst bed decreases with time. This could be explained by a shift in the reaction mechanism so more endothermic reaction steps are prevailing. The decrease in the bed temperature speeds up the deactivation by gum formation. This aspect of gum formation is also seen on the temperature profiles in Figure 9. Calculations with a heterogenous reactor model have shown that the decreasing minimum catalyst bed temperature could also be explained by a change of the effectiveness factors for the reactions. The radial poisoning profiles in the catalyst pellets influence the complex interaction between pore diffusion and reaction rates and this results in a shift in the overall balance between endothermic and exothermic reactions. 

Cao, C., Wang, Y., and Rozmiarek, R.T. Heterogeneous reactor model for steam reforming of methane in a microchannel reactor with microstructured catalysts. Catalysis Today, 2005,110 (1—2), 92. 

Estimate the limiting diffusion-reaction regimes under the prevailing lab reactor conditions for heterogeneous reactions, and use the appropriate lab reactor model. When possible, operate the reactor under kinetic control. 

The heterogeneous model is developed in terms of the bulk variables with the effectiveness factor introduced to account for the diffusional limitations. Certain assumptions have to be made for the overall reactor model, these are ... 

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